Mathematical Equivalence of Quantum and Classical Mechanics: A Proof-of-Concept for Reference Frame Representational Unity

We present a proof-of-concept demonstrating representational equivalence between quantum and classical mechanics through reference frame integration. By integrating a classical trajectory over all inertial reference frames, we derive the free-particle Schrödinger propagator, while projection onto a specific frame recovers the classical trajectory. We extend this analysis to celestial mechanics, showing that planets and galaxies would exhibit quantum behavior without the universal constancy of c. This bidirectional equivalence shows quantum and classical mechanics as convertible representations of the same reality, with extensions suggested in Spacetime Coherence Theory.